
Dear List,
I am trying to determine the best environmental predictors of the 
presence of a species along an elevational gradient.
Elevation ranges from 400 to 2050 m a.s.l. and the ratio of presences to 
absences is low (132 presences out 2800 samples)

So to start I fit the full model of with the variable of interest.

sc.m<-glm(PA~sp.max+su.mmin+su.max+fa.mmin+fa.max+Slope+Haupt4+Pop_density+Dist_G+Growi_sea+,data=sc.pa,'binomial')

First, I performed univariate and backward selection using Akaike 
Information Criteria, and the fit was good and realistic given my 
knowledge of the environment though the D^2 was low 0.08. My final model 
was:
---------------------------------
glm(formula = PA ~ Slope + sp.mmin + su.max + fa.mmin + Haupt4,
     family = "binomial", data = sc.pa)

Deviance Residuals:
     Min       1Q   Median       3Q      Max
-0.5415  -0.3506  -0.2608  -0.1762   3.0768

Coefficients:
              Estimate Std. Error z value Pr(>|z|)
(Intercept) -73.45212   23.13842  -3.174  0.00150 **
Slope        -0.03834    0.01174  -3.265  0.00109 **
sp.mmin     -15.34594    5.30360  -2.893  0.00381 **
su.max        5.09712    1.70332   2.992  0.00277 **
fa.mmin      13.52262    4.64021   2.914  0.00357 **
Haupt42      -0.72237    0.27710  -2.607  0.00914 **
Haupt43      -0.95730    0.37762  -2.535  0.01124 *
Haupt44      -0.25357    0.24330  -1.042  0.29731
---
     Null deviance: 958.21  on 2784  degrees of freedom
Residual deviance: 896.10  on 2777  degrees of freedom
AIC: 912.1

----------------------

I then realized that my residuals were all highly correlated (0.8-0.6) 
when I plotted them using acf() function.

So to account for this I used glmmPQL to fit the full model:

model.sc.c <- glmmPQL(PA ~ 
sp.mmin+su.mmin+su.max+fa.mmin+Slope+Haupt4+Pop_density+Dist_G+Growi_sea, random= 
~1|group.sc, data=sc.dat, family=binomial, correlation=corAR1())

However, the algorithm failed to converge and all the p-vaules were 
either 0 or 1 and coefficient estimates approached infinity. 
Additionally the grouping factor of the random effect is slightly 
arbitrary and accounts a tiny amount of variation.

---
So know I feel stuck between a rock and a hard place, on the one hand I 
know I have a lot of autocorrelation and on the other hand I don't have 
a clear way to include it in the model.

I would appreciate any advice on the matter.

Sincerely,

Tim

	[[alternative HTML version deleted]]

